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NASA NTRS1982

Adaptive control in the presence of unmodeled dynamics

Stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances were investigated. The class of adaptive algorithms considered are those commonly referred to as model reference adaptive control algorithms, self-tuning controllers, and dead beat adaptive controllers, developed for both continuous-time systems and discrete-time systems. A unified analytical approach was developed to examine the class of existing adaptive algorithms. It was discovered that all existing algorithms contain an infinite gain operator in the dynamic system that defines command reference errors and parameter errors; it is argued that such an infinite gain operator appears to be generic to all adaptive algorithms, whether they exhibit explicit or implicit parameter identification. It is concluded that none of the adaptive algorithms considered can be used with confidence in a practical control system design, because instability will set in with a high probability.

Rohrs, C. E.↗

NASA NTRS1984

Modular approach for satellite communication ground terminals

The trend in satellite communications is toward completely digital, time division multiple access (TDMA) systems with uplink and downlink data rates dictated by the type of service offered. Trunking terminals will operate in the 550 MBPS (megabit per second) region uplink and downlink, whereas customer premise service (CPS) terminals will operate in the 25 to 10 MBPS region uplink and in the 200 MBPS region downlink. Additional criteria for the ground terminals will be to maintain clock sychronization with the system and burst time integrity to within a matter of nanoseconds, to process required order-fire information, to provide adaptive data scrambing, and to compensate for variations in the user input output data rates, and for changes in range in the satellite communications links resulting from satellite perturbations in orbit. To achieve the required adaptability of a ground terminal to the above mentioned variables, programmable building blocks can be developed that will meet all of these requirements. To maintain system synchronization, i.e., all bursted data arriving at the satellite within assigned TDMA windows, ground terminal transmit data rates and burst timing must be maintained within tight tolerances. With a programmable synchronizer as the heart of the terminal timing generation, variable data rates and burst timing tolerances are achievable. In essence, the unit inputs microprocessor generated timing words and outputs discrete timing pulses.

Gould, G. R.↗

NASA NTRS1982

Robustness of adaptive control algorithms in the presence of unmodeled dynamics

This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally asymptotically stable under certain assumptions, the key ones being (1) that the number of poles and zeroes of the unknown plant are known, and (2) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be guide small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. Previously announced in STAR as N83-16061

Rohrs, C. E.↗

NASA NTRS1989

Six-degree-of-freedom aircraft simulation with mixed-data structure using the applied dynamics simulation language, ADSIM

A realistic simulation of an aircraft in the flight using the AD 100 digital computer is presented. The implementation of three model features is specifically discussed: (1) a large aerodynamic data base (130,00 function values) which is evaluated using function interpolation to obtain the aerodynamic coefficients; (2) an option to trim the aircraft in longitudinal flight; and (3) a flight control system which includes a digital controller. Since the model includes a digital controller the simulation implements not only continuous time equations but also discrete time equations, thus the model has a mixed-data structure.

Savaglio, Clare↗

NASA NTRS1990

Recent developments in learning control and system identification for robots and structures

This paper reviews recent results in learning control and learning system identification, with particular emphasis on discrete-time formulation, and their relation to adaptive theory. Related continuous-time results are also discussed. Among the topics presented are proportional, derivative, and integral learning controllers, time-domain formulation of discrete learning algorithms. Newly developed techniques are described including the concept of the repetition domain, and the repetition domain formulation of learning control by linear feedback, model reference learning control, indirect learning control with parameter estimation, as well as related basic concepts, recursive and non-recursive methods for learning identification.

Phan, M.↗

NASA NTRS1990

On modeling of integrated communication and control systems

The mathematical modeling scheme proposed by Ray and Halevi (1988) for integrated communication and control systems is considered analytically, with an emphasis on the effect of introducing varying and distributed time delays to account for asynchronous time-division multiplexing in the communication part of the system. Ray and Halevi applied a state-transition concept to transform the original continuous-time model into a discrete-time model; the same approach was used by Kalman and Bertram (1959) to model various types of sampled data systems which are not subject to induced delays. The relationship between the two modeling schemes is explored, and it is shown that, although the Kalman-Bertram method has the advantage of a unified approach, it becomes inconvenient when varying delays appear in the control loop.

Liou, Luen-Woei↗

NASA NTRS1991

Linear system theory

The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.

Callier, Frank M.↗

NASA NTRS1998

Interior Noise Reduction by Adaptive Feedback Vibration Control

The objective of this project is to investigate the possible use of adaptive digital filtering techniques in simultaneous, multiple-mode identification of the modal parameters of a vibrating structure in real-time. It is intended that the results obtained from this project will be used for state estimation needed in adaptive structural acoustics control. The work done in this project is basically an extension of the work on real-time single mode identification, which was performed successfully using a digital signal processor (DSP) at NASA, Langley. Initially, in this investigation the single mode identification work was duplicated on a different processor, namely the Texas Instruments TMS32OC40 DSP. The system identification results for the single mode case were very good. Then an algorithm for simultaneous two mode identification was developed and tested using analytical simulation. When it successfully performed the expected tasks, it was implemented in real-time on the DSP system to identify the first two modes of vibration of a cantilever aluminum beam. The results of the simultaneous two mode case were good but some problems were identified related to frequency warping and spurious mode identification. The frequency warping problem was found to be due to the bilinear transformation used in the algorithm to convert the system transfer function from the continuous-time domain to the discrete-time domain. An alternative approach was developed to rectify the problem. The spurious mode identification problem was found to be associated with high sampling rates. Noise in the signal is suspected to be the cause of this problem but further investigation will be needed to clarify the cause. For simultaneous identification of more than two modes, it was found that theoretically an adaptive digital filter can be designed to identify the required number of modes, but the algebra became very complex which made it impossible to implement in the DSP system used in this study. The on-line identification algorithm developed in this research will be useful in constructing a state estimator for feedback vibration control.

Lim, Tae W.↗

NASA NTRS1994

Measurand transient signal suppressor

A transient signal suppressor for use in a controls system which is adapted to respond to a change in a physical parameter whenever it crosses a predetermined threshold value in a selected direction of increasing or decreasing values with respect to the threshold value and is sustained for a selected discrete time interval is presented. The suppressor includes a sensor transducer for sensing the physical parameter and generating an electrical input signal whenever the sensed physical parameter crosses the threshold level in the selected direction. A manually operated switch is provided for adapting the suppressor to produce an output drive signal whenever the physical parameter crosses the threshold value in the selected direction of increasing or decreasing values. A time delay circuit is selectively adjustable for suppressing the transducer input signal for a preselected one of a plurality of available discrete suppression time and producing an output signal only if the input signal is sustained for a time greater than the selected suppression time. An electronic gate is coupled to receive the transducer input signal and the timer output signal and produce an output drive signal for energizing a control relay whenever the transducer input is a non-transient signal which is sustained beyond the selected time interval.

Bozeman, Richard J., Jr.↗

NASA NTRS1987

Issues in modeling and controlling the SCOLE configuration

The parametric study of the in-plane Spacecraft Control Laboratory Experiment (SCOLE) system, the Floquet Stability Analysis, and three dimensional formulations of the SCOLE system dynamics are examined. Control issues are discussed, such as: control of large structures with delayed input in continuous time; control with delayed input in discrete time; control law design for SCOLE using Linear Quadratic Gaussian (LQC)/TRR technique; and optimal torque control for SCOLE slewing maneuvers.

Bainum, Peter M.↗

NASA NTRS1991

Digital modelling, ideal state reconstructor, and control for time-delay sampled-data systems

The cascaded discrete-time state-space representation of a cascaded continuous-time system with fractional input delays is established. Based on the time-delay digital modelling, a practically implementable ideal state reconstructor is also established such that system states are exactly reconstructed via the measurement histories of inputs and outputs without a state observer. By utilizing the blockpulse function approximation the digital modelling of cascaded continuous-time systems with fractional input delays can be carried out, and an artificial input design method is proposed to determine the state feedback gain. Thus the practically implementable digital control law can be established for digital control of time-delay sampled-data systems. An illustrative example is shown to demonstrate the effectiveness of the proposed method.

Tsai, J. S. H.↗

NASA NTRS1983

Formulation of a practical algorithm for parameter estimation with process and measurement noise

A new formulation is proposed for the problem of parameter estimation in dynamic systems with both process and measurement noise. The formulation applies to continuous-time state space system models with discrete-time measurements. Previous formulations of this problem encountered several theoretical and practical difficulties which are overcome by the new formulation. The most important element of the new formulation is a reparameterization of the unknown noise covariances. A computer program that implements the new formulation is available.

Maine, R. E.↗

NASA NTRS1989

Computational issue in the analysis of adaptive control systems

Adaptive systems under slow parameter adaption can be analyzed by the method of averaging. This provides a means to assess stability (and instability) properties of most adaptive systems, either continuous-time or (more importantly for practice) discrete-time, as well as providing an estimate of the region of attraction. Although the method of averaging is conceptually straightforward, even simple examples are well beyond hand calculations. Specific software tools are proposed which can provide the basis for user-friendly environment to perform the necessary computations involved in the averaging analysis.

Kosut, Robert L.↗

NASA NTRS1991

A new finite element formulation for computational fluid dynamics. IX - Fourier analysis of space-time Galerkin/least-squares algorithms

A Fourier stability and accuracy analysis of the space-time Galerkin/least-squares method as applied to a time-dependent advective-diffusive model problem is presented. Two time discretizations are studied: a constant-in-time approximation and a linear-in-time approximation. Corresponding space-time predictor multi-corrector algorithms are also derived and studied. The behavior of the space-time algorithms is compared to algorithms based on semidiscrete formulations.

Shakib, Farzin↗

NASA NTRS1974

Program for the analysis of time series

A digital computer program for the Fourier analysis of discrete time data is described. The program was designed to handle multiple channels of digitized data on general purpose computer systems. It is written, primarily, in a version of FORTRAN 2 currently in use on CDC 6000 series computers. Some small portions are written in CDC COMPASS, an assembler level code. However, functional descriptions of these portions are provided so that the program may be adapted for use on any facility possessing a FORTRAN compiler and random-access capability. Properly formatted digital data are windowed and analyzed by means of a fast Fourier transform algorithm to generate the following functions: (1) auto and/or cross power spectra, (2) autocorrelations and/or cross correlations, (3) Fourier coefficients, (4) coherence functions, (5) transfer functions, and (6) histograms.

Brown, T. J.↗

NASA NTRS1972

On the input-output properties of linear time-invariant systems.

Recently improved sufficient conditions for the Lp stability of multiple-input multiple-output linear time-invariant feedback systems are given. The continuous-time case is done in detail; the discrete-time case is outlined. Unstable open-loop systems with singular residue matrices are allowed.

Desoer, C. A.↗

NASA NTRS1974

The use of precession modulation for nutation control in spin-stabilized spacecraft

The relations which determine the nutation effects induced in a spinning spacecraft by periodic precession thrust pulses are derived analytically. By utilizing the idea that nutation need only be observed just before each precession thrust pulse, a difficult continuous-time derivation is replaced by a simple discrete-time derivation using z-transforms. The analytic results obtained are used to develop two types of modulated precession control laws which use the precession maneuver to concurrently control nutation. Results are illustrated by digital simulation of an actual spacecraft configuration.

Taylor, J. M.↗

NASA NTRS1975

A study of sound generation in subsonic rotors, volume 2

Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation.

Chalupnik, J. D.↗